function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices. 
% 
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%

% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));

% Setup some useful variables
m = size(X, 1);
         
% You need to return the following variables correctly 
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a 
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the 
%               first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%
X = [ones(m, 1) X];
%5000*401
Y=zeros(m,num_labels);
delta1=zeros(size(Theta1));
delta2=zeros(size(Theta2));
for i=1:m
switch y(i)
case 10
Y(i,10)=1;
case 1
Y(i,1)=1;
case 2
Y(i,2)=1;
case 3
Y(i,3)=1;
case 4
Y(i,4)=1;
case 5
Y(i,5)=1;
case 6
Y(i,6)=1;
case 7
Y(i,7)=1;
case 8
Y(i,8)=1;
case 9
Y(i,9)=1;
end
end
z2=X*Theta1';
%5000*25
for i=1:m
for j=1:hidden_layer_size
a(i,j)=sigmoid(z2(i,j));
end
end
a2=[ones(m, 1) a];
%m*26
z3=a2*Theta2';
for i=1:m
for j=1:num_labels
a3(i,j)=sigmoid(z3(i,j));
end
end
q=max(a3, [], 2);
for i=1:m
for j=1:num_labels
if (a3(i,j)==q(i))
p(i)=j;
end
end
end
for i=1:m
for k=1:num_labels
J=J-Y(i,k)*log(a3(i,k))-(1-Y(i,k))*log(1-a3(i,k));
end
end
J=J/m;
T1=T2=0;
for i=1:hidden_layer_size
for j=2:(input_layer_size+1)
T1=T1+Theta1(i,j)^2;
end
end
for i=1:num_labels
for j=2:(hidden_layer_size+1)
T2=T2+Theta2(i,j)^2;
end
end
J=J+lambda*(T1+T2)/2/m;



% -------------------------------------------------------------
z22=[ones(m, 1) z2];
for t=1:m
d3(t,:)=a3(t,:)-Y(t,:);
d2(t,:)=d3(t,:)*Theta2.*sigmoidGradient(z22(t,:));%1*10 * 10*26 .* 26
delta1=delta1+d2(t,2:end)'*X(t,:);%25*1 * 1*401
delta2=delta2+d3(t,:)'*a2(t,:);
end
Theta1_grad=delta1/m;
Theta1_grad(:,2:end)=Theta1_grad(:,2:end)+lambda*Theta1(:,2:end)/m;
Theta2_grad=delta2/m;
Theta2_grad(:,2:end)=Theta2_grad(:,2:end)+lambda*Theta2(:,2:end)/m;
% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end
